Plant food. Refer to Problem 85 . The costs of the four mixes are Mix A , $46 ; Mix B , $72 ; Mix C , $57 ; and Mix D , $63 . Which of the solutions to Problem 85 would minimize the cost of the plant food?
Plant food. Refer to Problem 85 . The costs of the four mixes are Mix A , $46 ; Mix B , $72 ; Mix C , $57 ; and Mix D , $63 . Which of the solutions to Problem 85 would minimize the cost of the plant food?
Solution Summary: The author calculates the cost and ingredients of each type of plant food to minimize its cost.
Plant food. Refer to Problem
85
. The costs of the four mixes are Mix
A
,
$46
; Mix
B
,
$72
; Mix
C
,
$57
; and Mix
D
,
$63
. Which of the solutions to Problem 85 would minimize the cost of the plant food?
Let G be a graph with n ≥ 2 vertices x1, x2, . . . , xn, and let A be the adjacency matrixof G. Prove that if G is connected, then every entry in the matrix A^n−1 + A^nis positive.
Module Code: MATH380202
1. (a) Define the terms "strongly stationary" and "weakly stationary".
Let {X} be a stochastic process defined for all t € Z. Assuming that {X+} is
weakly stationary, define the autocorrelation function (acf) Pk, for lag k.
What conditions must a process {X+) satisfy for it to be white noise?
(b) Let N(0, 1) for t€ Z, with the {+} being mutually independent. Which of
the following processes {X+} are weakly stationary for t> 0? Briefly justify your
answers.
i. Xt for all > 0.
ii. Xo~N(0,) and X₁ = 2X+-1+ &t for t > 0.
(c) Provide an expression for estimating the autocovariance function for a sample
X1,..., X believed to be from a weakly stationary process. How is the autocor-
relation function Pk then estimated, and a correlogram (or acf plot) constructed?
(d) Consider the weakly stationary stochastic process ✗+ = + + +-1+ +-2 where
{E} is a white noise process with variance 1. Compute the population autocorre-
lation function Pk for all k = 0, 1, ....
iii)
i=5
x² = Σ
i=1
(Yi — mi)²
σ
2
By minimising oc², derive the formulae
for the best values of the model for
a 1 degree polynomial (2 parameters).
Chapter 4 Solutions
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